Nobel awarded to Roth and Shapley: Personal nostalgia

Today, the “Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel for 2012” was awarded to Alvin E. Roth and Lloyd S. Shapley“for the theory of stable allocations and the practice of market design”. As always when the Nobel is decided, I realize that I should not be one giving out the prize. Along with many, I try to make clever predictions, which always fail. On the other hand, when the prize is being awarded, I almost always find that the choice is obvious and natural.

This year is no exception. I will spare you for my failed prediction(s), but applaud this year’s choice. Roth and Shapley are both powerhouse scientists, and the research program that is being acknowledged today is really among the very basics of economics: Who trades with whom and why? To answer this, one has to make theories and predictions about how markets work, and to come up with mechanisms to solve allocation problems when the free market does not work.

Here, Shapley made the pure theory foundations (along with Gale) back in the 1960s, which Roth and others since the 1980s have applied to a host of real-life economic issues ranging from allocation of students to colleges to allocation of kidneys. A great lesson on how deep “theory-theory” can be adopted to very hands-on economic issues.

For me, it is a particular joy that Shapley gets the prize. In the 1950s, he developed a cooperative game concept called the Shapley value, which essentially through a single number ranks players’ value of participating in a game. The concept was applied to political decision making together with Martin Shubik in 1954, as the Shapley-Shubik index. It is a simple index that measures the voting power of parties, and, in particular, shows that number of seats in a committee or parliament is not the same as power. It is the power of the coalitions in which a party can be decisive, i.e., pivotal, that matters. Think of a parliament with three parties with 50, 49, and 1 votes, respectively. If only majority coalitions win, the party with 49 is pivotal in as many coalitions as the party with 1. Hence, these parties have the same power as measured by the Shapley-Shubik index. (The 50-vote party is pivotal in all three winning coalitions, and has thereby disproportionately more power than the party with just one vote less.)

I wrote my M.Sc. thesis on this index (and its subsequent derivatives) back in 1988, where I applied my own variant of it to power indices of parties in the Danish parliament in the 1970s and 1980s. Essentially, I just assigned priors to the likelihood of some coalitions to materialize—this contrasts with the derivation of the Shapley-Shubik index where all coalitions are equally likely. For Danes, it should not be surprising that it turned out that the small center party “Radikale Venstre” (which is neither radical, nor left winged) came out as having as much power as the big parties with the bulk of the seats in parliament. It was a slightly odd subject at a time where most wrote about exchange-rate target zones, but now, and particularly today, I am still quite happy about it.